Donald Trump has speculated that “rogue killers” may have been responsible for the presumed death of Jamal Khashoggi, as Turkish investigators finally gained access to the Saudi consulate, 13 days after the missing Washington Post columnist was last seen there.

Turkish officials were allowed into the consulate in Istanbul only after Saudi staff, consular visitors and a team of cleaners equipped with mops, buckets and disinfectant had been allowed into the building.

The investigators arrived in unmarked black cars late on Monday, and made no comment to journalists outside the consulate. As night fell, a crime scene truck arrived, along with a police car with Ankara plates.

Every now and again, a bewildered Saudi citizen poked his or her head out of the wrought iron gate, before running the gauntlet of dozens of cameras.

It was unclear what evidence might still be available, nearly two weeks after Khashoggi’s disappearance.

Saudi Arabia has angrily rejected any suggestion it was involved in interrogating Khashoggi, who had visited the consulate on a planned trip in relation to his forthcoming marriage. It has offered no explanation for his disappearance or any pictures of him leaving the consulate.

Turkey’s president, Recep Tayyip Erdoğan, and the Saudi monarch, King Salman, announced on Sunday night that a deal had been made for a “jointing working group” to examine the case, which gave a distinctly political feel to the probe.

Saudi officials arrive at the Saudi consulate in Istanbul to investigate the disappearance of journalist Jamal Khashoggi. Photograph: Tolga Bozoglu/EPA

The US president has threatened “severe punishment” if it turns out Khashoggi was killed in the consulate, but after speaking to the Saudi king by phone, Trump said on Monday that Salman “denies any knowledge of whatever may have happened” to the journalist.

“The denial was very, very strong,” Trump told reporters. “It sounded to me like maybe these could have been rogue killers. Who knows?”

“He told me in a very firm way that they had no knowledge of it. He said it very strongly,” Trump said.

The president’s claim that rogue elements may be responsible for Khashoggi’s disappearance implies he accepts that the journalist has been murdered – but is seeking a way out of the crisis that somehow absolves the Saudi royal court.

Turkey has already published details of a group of 15 men – some from Saudi intelligence – who arrived in Istanbul at the time of Khashoggi’s disappearance. Nine of the men arrived on a private jet from Riyadh.

The Trump administration is a close political and commercial ally of the Saudi kingdom and would prefer to smooth over the crisis in relations between Turkey, and Riyadh – but is also under pressure to ensure a credible investigations takes place.

The case has provoked an international outcry, with European allies urging “a credible investigation” and accountability for those responsible.

Google has become the latest company to pull out of a business conference in Saudi Arabia amid the turmoil. Google Cloud chief executive Diane Greene has followed others including figures from JP Morgan, Ford and Uber to say they would not attend the Future Investment Initiative Summit in Riyadh on 23 October.

Donald Trump said he had spoken to Saudi Arabia’s King Salman and that the US secretary of state, Mike Pompeo, would be meeting him. Photograph: Michael Reynolds/EPA

The kingdom agreed in principle on Friday to launch a joint investigation into Khashoggi’s disappearance in conjunction with Turkish police, but a search of the consulate was delayed by disagreements over the terms.

Turkish officers wanted to take in solvents to detect traces of blood, while the Saudis were insisting on a more limited search. Turkish sources repeated claims that it has audio of Khashoggi being killed inside the consulate, a revelation that implies the Turkish government was bugging the embassy.

How Jamal Khashoggi disappeared – visual guide

Turkish investigators believe Khashoggi was first interrogated in the consul general’s office on the building’s second floor, before being dragged into a second room, by a team of assassins. The Turkish team believe that his body was eventually dismembered in a third room.

A Saudi team that came to Turkey from Riyadh at the time of Khashoggi’s disappearance left hours after his presumed murder.

Khashoggi was a critic of the regime, in effect led by Mohammed Bin Salman since his father appointed him crown prince in June 2017. There have been suggestions Khashoggi was previously concerned he was about to be captured by the Saudi court.

Western diplomats have privately expressed concern that Saudi Arabia could have used the lengthy interim since 2 October to remove any traces of Khashoggi’s interrogation.

Lurid accounts of his alleged death have appeared in the Turkish press, based on apparent government sources, but ministers have been wary of repeating the claims in public.

Little has been said in public about the terms of reference of the joint Turkish-Saudi investigation, its timetable or likelihood of findings being published. Equally, no detail has been given concerning the internal investigation.

On Monday Turkish investigators – who had been willing to talk for much of the past nine days – were now more cautious. So too were Turkish journalists, one of whom said that his outlet had been instructed to focus less on the apparent crime and more on the political settlement.

The British foreign secretary, Jeremy Hunt, met his Turkish counterpart Mevlüt Çavuşoğlu on Monday and pledged support for a credible and thorough investigation into Khashoggi’s disappearance. After the meeting Hunt said the case was “deeply concerning”, adding: “The UK fully supports the Turkish investigation.”

The Turkish lira, under intense attack for months, strengthened on Monday, probably on news of a rapprochement between the US and Turkey, prompted by the Turkish court’s release of Andrew Brunson, a US pastor held in captivity for two years.

In a sign of possible tactical tensions within the kingdom, Saudi officials threatened reprisals against any country that imposed sanctions on Riyadh. However, its embassy in Washington later tweeted its gratitude to the US for showing restraint and not jumping to conclusions.

Saudi Embassy (@SaudiEmbassyUSA)

To help clarify recently issued Saudi statement, the Kingdom of Saudi Arabia extends it appreciation to all, including the US administration, for refraining from jumping to conclusions on the ongoing investigation. https://t.co/AhcsVkn7Cy